A higher-order generalization of an A₄⁽¹⁾-surface type q-Painlevé equation with \widetildeW((A_2N\rtimes A₁)⁽¹⁾× A₁⁽¹⁾) symmetry

2023/12/27 by Nobutaka Nakazono, Nakazono, Nobutaka
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2312.16431

openalex publication_date 2023/12/27 · openalex created_date 2023/12/30 · openalex updated_date 2026/07/28

Abstract

Recently, a birational representation of an extended affine Weyl group of (A_2N\rtimes A₁)⁽¹⁾-type, which gives a higher-order generalization of an A₄⁽¹⁾-surface type q-Painlevé equation, was obtained. In this paper, we extend it to a birational representation of an extended affine Weyl group of (A_2N\rtimes A₁)⁽¹⁾× A₁⁽¹⁾-type. Moreover, we provide conjectures on periodic reductions from systems of PΔEs with the CAC property to Painlevé type q-OΔEs.

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